The Residually Weakly Primitive Geometries of J 3

The residually weakly primitive geometries of HS

The Residually Weakly Primitive Geometries of M22

In [6], Dehon and the author described two algorithms to classify all geometries Γ of a given group G such that Γ is a firm and residually connected geometry and G acts flag-transitively and residually weakly primitively on Γ. We stated in that paper that these programs were able to classify all geometries with Borel subgroup not equal to the identity of G when G is the Hall-Janko group J2. In ...

Rank Three Residually Connected Geometries for M22, Revisited

The rank 3 residually connected flag transitive geometries Γ for M22 for which the stabilizer of each object in Γ is a maximal subgroup of M22 are determined. As a result this deals with the infelicities in Theorem 3 of Kilic and Rowley, On rank 2 and rank 3 residually connected geometries for M22. Note di Matematica, 22(2003), 107–154.

A Generalization of a Construction due to Van Nypelseer

We give a construction leading to new geometries from Steiner systems or arbitrary rank two geometries. Starting with an arbitrary rank two residually connected geometry Γ, we obtain firm, residually connected, (IP )2 and flagtransitive geometries only if Γ is a thick linear space, the dual of a thick linear space or a (4, 3, 4)-gon. This construction is also used to produce a new firm and resi...

A class of J-quasipolar rings

In this paper, we introduce a class of $J$-quasipolar rings. Let $R$ be a ring with identity. An element $a$ of a ring $R$ is called {it weakly $J$-quasipolar} if there exists $p^2 = pin comm^2(a)$ such that $a + p$ or $a-p$ are contained in $J(R)$ and the ring $R$ is called {it weakly $J$-quasipolar} if every element of $R$ is weakly $J$-quasipolar. We give many characterizations and investiga...